159k views
5 votes
If a and b are integers and 71 < ab < 76, then all of the following could be the values of b except: (A) 18 (B) 8 (C) 12 (D) 7 (E) 5

1 Answer

5 votes

We are given that

a and b are integers and 71 < ab < 76

We will check each options

option-A:

b=18

we can plug it


71<a(18)<76

we can divide both sides by 18


(71)/(18) <b<(76)/(18)

now, we can simplify it


3.944<a<4.222

Since, 'a' is a integer

so, a=4 lies on interval

so, this interval is true

so, this is FALSE

option-B:

b=8

we can plug it


71<a(8)<76

we can divide both sides by 8


(71)/(8) <b<(76)/(8)

now, we can simplify it


8.875<a<9.5

Since, 'a' is a integer

so, a=9 lies on interval

so, this interval is true

so, this is FALSE

option-C:

b=12

we can plug it


71<a(8)<76

we can divide both sides by 12


(71)/(12) <b<(76)/(12)

now, we can simplify it


5.9166<a<6.333

Since, 'a' is a integer

so, a=6 lies on interval

so, this interval is true

so, this is FALSE

option-D:

b=7

we can plug it


71<a(5)<76

we can divide both sides by 7


(71)/(7) <b<(76)/(7)

now, we can simplify it


10.14285<a<10.857

Since, 'a' is a integer

so, no integer lies on this interval

so, this interval is false

so, this is TRUE

option-E:

b=5

we can plug it


71<a(5)<76

we can divide both sides by 5


(71)/(5) <b<(76)/(5)

now, we can simplify it


14.2<a<15.2

Since, 'a' is a integer

so, a=15

so, this interval is true

so, this is FALSE


User Jpihl
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories